How is the time registration arrange on a satelite? Is it arranged with an electronic, electrical circuit? Is it arranhed with an atomic clock or a laser?

Satellites use multiple, layered mechanisms for timekeeping. Here is the clear structure:

**1. What provides the official time on satellites? → Atomic clocks**

Most navigation and scientific satellites (GPS, Galileo, GLONASS, BeiDou, ESA deep-space missions) carry atomic clocks.

Typical atomic clocks used:

Cesium atomic clocks
Rubidium atomic clocks (most common in GPS)
Hydrogen maser clocks (Galileo, ESA deep-space)
Laser-pumped atomic clocks (modern, more stable)

These clocks define the satellite’s internal “master time” with accuracies around 10⁻¹² to 10⁻¹⁵.

So the time generation is done by atomic transitions, not electronics alone.

2. What electronics do inside the satellite

Although time originates from the atomic clock, electronics are used for:

✔ Frequency synthesis

Electronic circuits divide or multiply the atomic frequency into:

10.23 MHz (GPS)
10 MHz, 100 MHz, etc.

✔ Distributing the clock

Through low-jitter electrical lines and clock distribution boards.

✔ Phase-locked loops (PLLs)

Electronic PLLs keep derived clocks synchronised to the atomic standard.

✔ Redundancy switching

Satellites usually carry multiple atomic clocks that can be hot-swapped by electronics if one begins drifting.

So, electronics route and maintain the timing, but do not generate the absolute time.

3. Are lasers involved?

Yes, but only in advanced atomic clocks:

Laser-cooled atomic clocks

Used in:

ESA Galileo IOV + FOC satellites (Passive Hydrogen Maser uses microwave, but next-gen uses lasers)
NASA deep-space atomic clock (DSAC)
Laboratory clocks becoming space-ready (optical clocks)

Lasers are used to:

cool atoms
manipulate atomic states
interrogate optical transitions

But they are part of the atomic clock, not a separate timing method.

4. Summary

Component	Function
Atomic clock	Primary time reference (Rubidium, Cesium, Hydrogen Maser, optical/laser-pumped).
Electronics	Distribute, stabilize, and use the atomic clock signal.
Lasers	Used inside modern atomic clocks (optical clocks, laser pumping, cooling).
No normal electrical oscillator alone	Not accurate enough → would drift meters per second for GPS.

If you want it very concise

A satellite keeps time with an atomic clock.
Electronics distribute and stabilize the signal.
Lasers are used inside advanced atomic clocks.

If you want, I can also explain:

why relativistic corrections must be applied (+38 µs/day)
how GPS satellites synchronise time with Earth
how the clock signal is encoded in the radio navigation message.

Is this:[These clocks define the satellite’s internal “master time” with accuracies around 10⁻¹² to 10⁻¹⁵.] seconds

Yes — those numbers refer to fractional time accuracy, meaning seconds per second.

Here is what they mean:

✔ 10⁻¹² to 10⁻¹⁵ accuracy = time error of one part in 1,000,000,000,000 to 1,000,000,000,000,000

This is a dimensionless fraction, but its effect is on seconds.

Example:

A clock with 10⁻¹² stability drifts about
1 picosecond (10⁻¹² s) per second
A clock with 10⁻¹⁵ stability drifts about
1 femtosecond (10⁻¹⁵ s) per second

✔ Converting this to time drift per day

Stability	Drift per day
10⁻¹²	~100 nanoseconds/day
10⁻¹³	~10 nanoseconds/day
10⁻¹⁴	~1 nanosecond/day
10⁻¹⁵	~0.1 nanosecond/day

GPS needs accuracy around 1–10 nanoseconds, so this matches well.

✔ Why it matters

1 nanosecond of timing error → 30 cm of position error.
So atomic clocks with 10⁻¹³ or better stability keep GPS distances accurate.

✔ Short answer

Yes, the 10⁻¹² to 10⁻¹⁵ refers to the time error in seconds, expressed as a fractional stability per second.

If you want, I can also:

convert this to frequency accuracy (Hz)
show how this determines GPS position accuracy
show how the relativistic correction of +38 µs/day compares to these tiny errors.

Time on the satelite goes, progresses slower on the satelite depending on the distance from the earth's core. Can you give me the law as a function of this distance and everything that influences it?

Yes — we can write the exact physical law for how a satellite’s clock runs slower or faster depending on distance from Earth’s center, including all physical influences.

Below is the clean GR-correct formula.

✅ 1. GR: Gravitational time dilation as a function of distance

For a non-rotating, spherically symmetric Earth (Schwarzschild metric), the rate of a clock at radius $r$ compared to a clock far away is:

\frac{d\tau}{dt} = \sqrt{1-\frac{2GM}{rc^2}}

Where:

$d\tau$ = proper time on the satellite
$dt$ = coordinate time far from gravity
$G$ = gravitational constant
$M$ = Earth’s mass
$r$ = distance from Earth’s center
$c$ = speed of light

For small potentials (true for Earth), this can be approximated:

\frac{d\tau}{dt} \approx 1 - \frac{GM}{rc^2}

This shows the fundamental dependence: higher altitude → less gravitational potential → time runs faster.

✅ 2. Include the satellite's orbital velocity

A moving clock suffers special relativistic time dilation:

\frac{d\tau}{dt} = \sqrt{1 - \frac{v^2}{c^2}}

A satellite moves fast → its time runs slower.

✅ 3. Full equation combining GR + SR (used for GPS satellites)

The complete expression to first order (valid for Earth satellites):

\frac{d\tau}{dt} \approx 1 -\frac{GM}{rc^{2}} -\frac{v^{2}}{2c^{2}}

This is the actual formula used for GPS relativistic corrections.

Meaning:

Term 1: $-\frac{GM}{rc^2}$ → GR gravitational time dilation
Term 2: $-\frac{v^2}{2c^2}$ → SR velocity time dilation

These two effects compete:

Gravity makes the satellite’s clock run faster.
Speed makes it run slower.

For GPS, the net effect is +38 microseconds/day faster than Earth clocks.

✅ 4. All influences on time progression (complete list)

Main GR + SR effects

Gravitational time dilation
$-\frac{GM}{rc^2}$
Velocity time dilation
$-\frac{v^2}{2c^2}$

Secondary effects

Earth’s rotation (centrifugal potential)
Affects ground clocks, not satellites.
Earth’s quadrupole moment (J₂ term)
Corrections from Earth not being perfectly spherical.
(Very small but used in precision models.)
Orbit eccentricity corrections
Clock rate oscillates slightly over its orbit.
Applied continuously in GPS.
Relativistic frequency shift of the onboard oscillator
Already pre-corrected before launch.

✅ **5. The most complete standard law (used in GPS ICD)**

The GPS relativistic correction term for a satellite in elliptical orbit is:

\Delta t_r = -\frac{2}{c^2} \, \mathbf{r}\cdot\mathbf{v}

This accounts for:

gravitational potential
orbital velocity
orbital eccentricity

It is the operational formula.

If you want:

I can also compute:

the exact time dilation for any satellite altitude you choose
the difference in seconds/day directly
a graph of time dilation vs. radius (if you want a plot)

Just tell me the altitude or “make the graph”.

How much is c^2/GM and what is the distance for a geostationair statelite and most other statelites?

Nice question — let’s put numbers on it.

Key constant you asked for

Using
$G=6.67430\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}$ ,
$M_\oplus=5.97219\times10^{24}\,\mathrm{kg}$ ,
$c=299\,792\,458\ \mathrm{m/s}$ :

$\displaystyle \frac{c^{2}}{GM}\approx 225.4769\ \mathrm{m^{-1}}$
(about 225.48 per metre)

Equivalently it’s useful to give the small length scale $GM/c^{2}$ :

$\displaystyle \frac{GM}{c^{2}}\approx 0.00443504\ \mathrm{m}$ ≈ 4.435 mm.
(This is the Earth’s gravitational radius — extremely small.)

Typical satellite distances (approx.)

Earth mean radius: $R_\oplus \approx 6\,371\ \mathrm{km}$ .
Geostationary altitude above Earth surface: $\approx 35\,786\ \mathrm{km}$ → radius $r_{\rm GEO}\approx 42\,157\ \mathrm{km}$ (≈ $4.2157\times10^{7}$ m).
GPS / MEO altitude: ≈ $20\,200\ \mathrm{km}$ → radius ≈ $26\,571\ \mathrm{km}$ .
LEO typical altitudes: roughly $200$ – $2\,000\ \mathrm{km}$ → radii ~ $6.6\times10^{6}$ – $8.4\times10^{6}$ m. (ISS ≈ 400 km altitude.)

Useful dimensionless numbers (appear in GR formulas like $GM/(rc^{2})$ )

$GM/(R_\oplus c^2)$ (at Earth's surface) ≈ $6.96\times10^{-10}$ .
$GM/(r_{\rm GEO} c^2)$ ≈ $1.05\times10^{-10}$ .
$GM/(r_{\rm GPS} c^2)$ ≈ $1.67\times10^{-10}$ .
For LEO (~400 km) $GM/(r c^2)$ ≈ $6.55\times10^{-10}$ .

These are tiny numbers; they are the terms that enter the approximate gravitational time-dilation formula
$\;d\tau/dt\approx 1 - GM/(rc^{2})\;$ (first-order).

Example: how much faster a GEO clock runs vs a surface clock (gravitational part)

Difference of the gravitational term between surface and GEO:

$\Delta\!\bigl(GM/(rc^2)\bigr) \approx 5.91\times10^{-10}$ (surface minus GEO)
That corresponds to ≈ 5.11×10⁻⁵ s/day ≈ 51.1 microseconds per day (gravitational effect alone — GEO clocks run faster).

If you include the special-relativistic slowdown from GEO orbital speed (~3.07 km/s), that removes ≈ 4.5 μs/day, leaving a net of ≈ +46.6 μs/day (GEO clock faster than ground clock).

(For comparison: GPS satellites end up about +38 μs/day net after both effects and other small corrections.)

How to use $\dfrac{c^2}{GM}$

Because $\dfrac{c^2}{GM}$ ≈ 225.48 m⁻¹, you can quickly convert between the dimensionless potential and a length:

\frac{GM}{rc^2} = \frac{GM/c^2}{r} \quad\text{with }GM/c^2\approx0.004435\ \mathrm{m}.

So for any radius $r$ (in metres) just compute $0.004435\!/r$ to get $GM/(rc^2)$ .

If you want, I can:

compute the exact seconds/day difference for any specific satellite altitude you give, or
make a graph of time-dilation (seconds/day) vs altitude from surface up to GEO.

Are the times on statelites correct per day?

Yes — satellite times are correct per day, but only because they are actively corrected.
If we did nothing, satellite clocks would drift badly compared to clocks on Earth.

Let me explain clearly.

✅ 1. Raw satellite clocks would be WRONG per day

A satellite clock naturally experiences:

✔ Gravitational time dilation (runs faster)

Higher altitude → weaker gravity → clock gains time.

✔ Special relativistic time dilation (runs slower)

High orbital speed → clock loses time.

Net effect per day:

GPS satellites: would run +38 microseconds/day faster
GEO satellites: would run ≈ +46 microseconds/day faster
LEO satellites: usually run slower, because speed dominates

If left uncorrected, this would cause:

GPS position errors of about 10 km per day
Navigation would become useless in minutes

So the “raw” satellite time is not naturally correct.

✅ 2. How satellites are made correct

Method 1 — Pre-launch frequency offset

GPS atomic clocks are deliberately detuned on Earth before launch.

GPS onboard clock frequency:

f_\text{space} = f_\text{ground} \left(1 - 4.4647\times10^{-10}\right)

This offset exactly cancels the +38 µs/day relativistic gain once the satellite is in orbit.

This means:

On Earth: the clock is wrong
In orbit: it becomes correct

Method 2 — Continuous correction from Earth

Every navigation satellite (GPS, Galileo, GLONASS, BeiDou):

Has its clock monitored from ground stations
Receives correction updates several times per day
Broadcasts its “clock correction parameters” in the navigation signal

So the system always knows:

the clock bias
the clock drift
the clock drift rate

And corrects for all of them in real time.

✅ 3. Are satellite clocks correct at any moment?

✔ The system time (GPS Time, Galileo Time) is correct

✔ The broadcast signal, after applying the correction parameters, is correct

✔ The physical onboard clock is never perfect

but the system mathematically removes its errors.

This is how GPS gives meter-level precision.

✔ Final answer

Satellite clocks, by themselves, run incorrectly per day.
But the navigation system corrects them continuously so that the effective time is accurate to nanoseconds.

If you want, I can compute:

how many meters of error a 1-nanosecond clock error creates
the exact drift per day for any satellite you choose
a graph showing how the raw clock behaves vs the corrected clock.

this:[Gravity makes the satellite’s clock run faster.] is not clear. The futher away from a gravity source the faster the clock runs.

You are 100% correct, and let me restate it clearly so there is zero ambiguity:

✅ The farther a clock is from a gravity source, the faster it runs.

This is the core statement of gravitational time dilation.

So:

A clock near Earth’s surface runs slower.
A clock high above Earth (like on a satellite) runs faster.

This comes directly from General Relativity.

Why my sentence means the same thing (but can be worded better)

I wrote:

“Gravity makes the satellite’s clock run faster.”

What this should be read as is:

“The weaker gravitational field at the satellite’s distance makes the satellite’s clock run faster than a clock on Earth’s surface.”

But the shorter wording can be misread.
So your interpretation is correct.

Let me rewrite the principle in the clearest possible form:

✔ Correct GR statement

The rate of a clock increases as gravitational potential increases.

Since gravitational potential increases with distance from the mass,
a clock higher up runs faster.

Mathematically:

\frac{d\tau}{dt} \approx 1 - \frac{GM}{rc^2}

If $r$ (distance from Earth’s center) increases → the term $GM/(rc^2)$ becomes smaller, so the clock rate $d\tau/dt$ becomes closer to 1, meaning:

👉 The clock runs faster.

✔ Example: Earth surface vs GPS altitude

Earth surface clock runs slower
GPS satellite clock runs 45.9 microseconds/day faster (gravitational only)

Then subtract the SR effect (satellite speed slows the clock by 7.0 μs/day):

Final net:
+38.9 μs/day faster than Earth clocks.

If you want, I can express this using your ontology framework too:

A lower gravitational potential corresponds to a different second-length,

and the “local time derivative” belongs to a different relation equation.

Just tell me if you want it written in your ontology format.

Je zei:

ChatGPT zei:

1. What provides the official time on satellites? → Atomic clocks

2. What electronics do inside the satellite

✔ Frequency synthesis

✔ Distributing the clock

✔ Phase-locked loops (PLLs)

✔ Redundancy switching

3. Are lasers involved?

Laser-cooled atomic clocks

4. Summary

If you want it very concise

Je zei:

ChatGPT zei:

✔ 10⁻¹² to 10⁻¹⁵ accuracy = time error of one part in 1,000,000,000,000 to 1,000,000,000,000,000

Example:

✔ Converting this to time drift per day

✔ Why it matters

✔ Short answer

Je zei:

ChatGPT zei:

✅ 1. GR: Gravitational time dilation as a function of distance

✅ 2. Include the satellite's orbital velocity

✅ 3. Full equation combining GR + SR (used for GPS satellites)

Meaning:

✅ 4. All influences on time progression (complete list)

Main GR + SR effects

Secondary effects

✅ 5. The most complete standard law (used in GPS ICD)

If you want:

Je zei:

ChatGPT zei:

Key constant you asked for

Typical satellite distances (approx.)

Useful dimensionless numbers (appear in GR formulas like GM/(rc2)GM/(rc^{2})GM/(rc2))

Example: how much faster a GEO clock runs vs a surface clock (gravitational part)

How to use c2GM\dfrac{c^2}{GM}GMc2​

Je zei:

ChatGPT zei:

✅ 1. Raw satellite clocks would be WRONG per day

✔ Gravitational time dilation (runs faster)

✔ Special relativistic time dilation (runs slower)

Net effect per day:

✅ 2. How satellites are made correct

Method 1 — Pre-launch frequency offset

Method 2 — Continuous correction from Earth

✅ 3. Are satellite clocks correct at any moment?

✔ The system time (GPS Time, Galileo Time) is correct

✔ The broadcast signal, after applying the correction parameters, is correct

✔ The physical onboard clock is never perfect

✔ Final answer

Je zei:

ChatGPT zei:

✅ The farther a clock is from a gravity source, the faster it runs.

Why my sentence means the same thing (but can be worded better)

✔ Correct GR statement

The rate of a clock increases as gravitational potential increases.

✔ Example: Earth surface vs GPS altitude

A lower gravitational potential corresponds to a different second-length,

**1. What provides the official time on satellites? → Atomic clocks**

✅ **5. The most complete standard law (used in GPS ICD)**

Useful dimensionless numbers (appear in GR formulas like $GM/(rc^{2})$ )

How to use $\dfrac{c^2}{GM}$